Vehicle Routing & Scheduling

1. Vehicle Routing & Scheduling • Cluster Algorithms • Improvement Heuristics • Time Windows

2. Cluster Algorithms • Select certain customers as seed points for routes. • Farthest from depot. • Highest priority. • Equally spaced. • Grow routes starting at seeds. Add customers: • Based on nearest neighbor or nearest insertion • Based on savings. • Based on minimum angle. • Re-optimize each route (solve a TSP for customers in each route).

3. depot Add nearest neighbor Cluster with Nearest Neighbor Suppose each vehicle capacity = 4 customers depot Select 3 seeds

4. depot Add nearest neighbor Cluster with Nearest Neighbor Suppose each vehicle capacity = 4 customers depot Add nearest neighbor

5. VRP Improvement Heuristics • Start with a feasible route. • Exchange heuristics within a route. • Switch position of one customer in the route. • Switch 2 arcs in a route. • Switch 3 arcs in a route. • Exchange heuristics between routes. • Move a customer from one route to another. • Switch two customers between routes.

6. Improved route 3 1 2 4 5 depot 6 K-opt Exchange • Replace k arcs in a given route by k new arcs so the result is a route with lower cost. • 2-opt: Replace 4-5 and 3-6 by 4-3 and 5-6. Original route 3 1 2 4 5 depot 6

7. Improved route 3 1 2 5 4 depot 6 3-opt Exchange • 3-opt: Replace 2-3, 5-4 and 4-6 by 2-4, 4-3 and 5-6. Original route 3 1 2 5 4 depot 6

8. Improvement Heuristics Cluster with Nearest Neighbor depot depot Starting routes “Optimized” routes

9. Time Windows • Problems with time windows involve routing and scheduling. 3,[2-4] 3,[2-4] 1, [9-12] 2,[1-3] 4,[10-2] 5,[8-10] Customer number depot 6,[9-12] Start and end of time window (2:00 pm - 4:00 pm)

10. Clustering and Time Windows • Cluster customers based on location and time window. • Design routes for each cluster. 3,[2-4] 1, [9-12] 2,[1-3] 4,[3-5] 5,[8-11] depot 6,[9-12]

11. Savings Method with Time Windows • Start with n one stop routes from depot to each customer. • Calculate all savings for joining two customers and eliminating a trip back to the depot. • Sij = Ci0 + C0j - Cij • Order savings from largest to smallest. • Form route by linking customers according to savings if time windows are satisfied.

12. Savings Method with Time Windows • Order savings from largest to smallest. • S35 • S34 • S45 • S36 • S56 • S23 • S46 • S24 • S25 • S12 • S26 • S13 • etc.

13. Savings Method with Time Windows One hour travel time between any two customers. Half hour delivery time at each customer. Largest savings = S35 Leave depot: 10:00 Arrive at 5: 11:00 Leave 5: 11:30 Arrive at 3: 2:00 3,[2-4] 1, [9-12] 2,[1-3] 4,[10-2] 5,[8-11] Next largest savings: S34 , S45 ,S36 ,S56 depot 6,[9-12]

14. Savings Method with Time Windows One hour travel time between any two customers. Half hour delivery time at each customer. S56 Leave depot: 8:30 Arrive at 6: 9:30 Leave 6: 10:00 Arrive at 5: 11:00 Leave 5: 11:30 Arrive at 3: 2:00 3,[2-4] 1, [9-12] 2,[1-3] 4,[10-2] 5,[8-11] depot Next largest savings: S23 , S46 , S24 6,[9-12]

15. Savings Method with Time Windows One hour travel time between any two customers. Half hour delivery time at each customer. Leave depot: 8:30 Arrive at 6: 9:30 Leave 6: 10:00 Arrive at 5: 11:00 Leave 5: 11:30 Arrive at 3: 2:00 Leave depot: 12:30 Arrive at 4: 1:30 Leave 4: 2:00 Arrive at 2: 3:00 S24 3,[2-4] 1, [9-12] 2,[1-3] 4,[10-2] 5,[8-11] Need S16 or S14. Will customer 1 fit on black or red route? depot 6,[9-12]

16. Savings Method with Time Windows One hour travel time between any two customers. Half hour delivery time at each customer. Leave depot: 8:30 Arrive at 6: 9:30 Leave 6: 10:00 Arrive at 5: 11:00 Leave 5: 11:30 Arrive at 3: 2:00 S14 3,[2-4] 1, [9-12] 2,[1-3] 4,[10-2] Leave depot: 11:00 Arrive at 1: 12:00 Leave 1: 12:30 Arrive at 4: 1:30 Leave 4: 2:00 Arrive at 2: 3:00 5,[8-11] depot 6,[9-12]